Penalized likelihood methods for modeling count data

The paper considers parameter estimation in count data models using penalized likelihood methods. The motivating data consists of multiple independent count variables with a moderate sample size per variable. The data were collected during the assessment of oral reading fluency (ORF) in school-aged children. A sample of fourth-grade students were given one of ten available passages to read with these differing in length and difficulty. The observed number of words read incorrectly (WRI) is used to measure ORF. Three models are considered for WRI scores, namely the binomial, the zero-inflated binomial, and the beta-binomial. We aim to efficiently estimate passage difficulty, a quantity expressed as a function of the underlying model parameters. Two types of penalty functions are considered for penalized likelihood with respective goals of shrinking parameter estimates closer to zero or closer to one another. A simulation study evaluates the efficacy of the shrinkage estimates using Mean Square Error (MSE) as metric. Big reductions in MSE relative to unpenalized maximum likelihood are observed. The paper concludes with an analysis of the motivating ORF data.

Disentangling key species interactions in diverse and heterogeneous communities: A Bayesian sparse modelling approach

Modelling species interactions in diverse communities traditionally requires a prohibitively large number of species‐interaction coefficients, especially when considering environmental dependence of parameters. We implemented Bayesian variable selection via sparsity‐inducing priors on non‐linear species abundance models to determine which species interactions should be retained and which can be represented as an average heterospecific interaction term, reducing the number of model parameters. We evaluated model performance using simulated communities, computing out‐of‐sample predictive accuracy and parameter recovery across different input sample sizes. We applied our method to a diverse empirical community, allowing us to disentangle the direct role of environmental gradients on species’ intrinsic growth rates from indirect effects via competitive interactions. We also identified a few neighbouring species from the diverse community that had non‐generic interactions with our focal species. This sparse modelling approach facilitates exploration of species interactions in diverse communities while maintaining a manageable number of parameters.